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A park in a subdivision is triangular-shaped. Two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58 degrees. To the nearest unit, find the area of the park in square yards.

A32,557 yd2
B14,470 yd2
C28,940 yd2
D43,410 yd2

Verified Answer :

scme1702

First, we convert the lengths of the sides from feet to yards:
573 ft = 191 yd
536 ft = 178.7 yd
Area of a triangle is given by:
1/2 absin(C)
A = 1/2 x 191 x 178.7 x sin(58)
A = 14,473 sq yd
The answer is B.

Answer:

Option (b) is correct.

The area of the park is  14,470 square yards.

Step-by-step explanation:

Given :  A park in a subdivision is triangular-shaped. Two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58°.

We have to find the area of the park in square yards.

Since, Given two adjacent sides of the park are 573 feet and 536 feet. The angle between the sides is 58°.

Area of triangle = \(\frac{1}{2}\cdot a \cdot b\cdot \sin\theta\),

where \(\theta\) is the angle between sides a and b.

Substitute,  a = 573 , b = 536 and \(\theta=58^{\circ}\)

Area of triangle = \(\frac{1}{2}\cdot 573 \cdot 536 \cdot \sin(58^{\circ})\)

Simplify, we have,

Area of triangle = \(130229.66\) ft²

Also, 1 feet square = 0.111111 yard square

130229.66 feet square = 14469.96 yard square

Thus, The area of the park is  14,470 square yards.

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